Probability & Statistics for Engineers I

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Probability & Statistics for Engineers I

• Introduction to Statistics
• Concept of Data and Variables
• Data Collection and Descriptive Statistics
• Inferential Statistics
• Populations and Samples
• Descriptive Statistics
• Frequency Tables and Graphs
• Relative Frequency Tables and Graphs
• Grouped Data, Histograms
• Ogives, Stem and Leaf Plots
• Sample Mean, Sample Median, Sample Mode
• Sample Variance and Standard Deviation
• Sample Percentiles and Box Plots
• Chebyshev’s Inequality
• Normal Data Sets
• Paired Data Set
• Sample Correlation Coefficient
• Elements of Probability
• Basic Terminology in Probability
• Sample Space and Events
• Venn Diagrams and Algebra of Events
• Axioms of Probability
• Conditional Probability
• Bayes’ Theorem and Independent Events
• Random Variables and Expectation
• Random Variables, Types of Random Variables
• Jointly Distributed Random Variables
• Expectation
• Property of Expected Values
• Use of Expected Values in Decision Making
• Variance, Covariance
• Variance of Sums of Random Variables
• Moment Generating Functions
• Special Random Variables
• Binomial Random Variables
• Poisson Random Variables
• Uniform Random Variables
• Normal Random Variables
• Exponential Variables
• Gamma Distribution
• Chi-Square Distribution
• t-Distribution and F-Distribution
• Distributions of Sampling Statistics
• Central Limit Theorem
• Sampling Distribution for Normal Population
• Sampling from a Finite Population
• Parameter Estimation
• Maximum Likelihood Estimators
• Interval Estimates
• Estimating the difference in Means of Two Normal Population
• Approximate Confidence Interval for the Mean
• Confidence Interval of the Mean of Exponential Distribution
• Bayes’ Estimator